First-half goals from Daniel Ayala and Adama Traore were followed by a third from Patrick Bamford after the restart to put Boro on course for three points against the Tykes.
But Barnsley pulled one back through Keiffer Moore and for the last 32 minutes there were real signs the visitors could have made an even closer game of it.
In the end Middlesbrough stayed resilient to claim the victory, thus climbing three points clear of seventh-placed Bristol City and remaining in the play-off places.
Pulis said: “In the first half we did very well, passed it well, played through the pitch and put lots of crosses in. The one disappointment was that we never scored more goals.
“The third goal should have truthfully killed it but we took our foot off the pedal and that’s one of the things we’ve been talking about. You can’t do that at any level.
“You’ve got to make sure you keep your foot on the pedal. It’s been a tough week, three really tough games and we’ve got the points we want and need so I can’t be too harsh on them.
“The challenge is to stay in there now. As I’ve said, we can work all week but once they cross that line they take responsibility and it’s up to the players. A lot of things are said about managers and coaches... but they have to take responsibility.
“In the next nine games we’ll see. I don’t know what their characters are like because I’ve not brought them in, but they’ve done fantastically since I came here and now we’ll see what happens and try to keep it going.”
While Middlesbrough are looking to secure a swift return to the Premier League, Barnsley remain deep in relegation trouble.
A haul of just one win from 10 games leaves them just a couple of points above the bottom three.
Tykes boss Jose Morais, who has won one of his five matches in charge, said: “We knew it was a difficult opponent, with quality players.
“We were aware of situations that could happen in the game and for some reason we didn’t control it in a good way in the beginning and I believe in the first half we had problems to keep our organisation.
“This has happened in some games, we wanted to correct it and we couldn’t.
“I wasn’t impressed with the second half, I was surprised with the first half. I believed the team can do what they did in the second half.
“That is what I wanted and the players wanted, we wanted that for the whole game. That is what we have to work on to achieve the results we want in such a competitive league with opponents who have quality.
“I’m aware of what we need to do to be in a better position. We have played four games away, we knew this was against Middlesbrough, a good team with good players, a team that has been improving.
“Most players here have played in the Premier League. To play against good teams is when you can be extraordinary and this was an opportunity to do it... we couldn’t do it but we have other games to play and I believe they can do what they can.”